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Define a set X recursively as follows. В. 3 and 7 are in X. R. if x and y are in X, so is x + y. (Here it is possible that x = y) Prove that, for every natural number n> 12, n E X.

Define a set X recursively as follows. В. 3 and 7 are in X. R. if x and y are in X, so is x + y. (Here it is possible that x = y) Prove that, for every natural number n> 12, n E X.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Definition of the Set X** The set \( X \) is defined recursively with the following rules: 1. **Base Case (B):** The numbers 3 and 7 are included in the set \( X \). 2. **Recursive Case (R):** If \( x \) and \( y \) are elements in the set \( X \), then their sum \( x + y \) is also in the set \( X \). It is permissible that \( x = y \). --- **Assertion to Prove** Prove that for every natural number \( n \geq 12 \), \( n \) is an element of the set \( X \).
Transcribed Image Text:**Definition of the Set X** The set \( X \) is defined recursively with the following rules: 1. **Base Case (B):** The numbers 3 and 7 are included in the set \( X \). 2. **Recursive Case (R):** If \( x \) and \( y \) are elements in the set \( X \), then their sum \( x + y \) is also in the set \( X \). It is permissible that \( x = y \). --- **Assertion to Prove** Prove that for every natural number \( n \geq 12 \), \( n \) is an element of the set \( X \).
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